Define the twin prime constant C < sub > 2 </ sub > as

Define C < sub > 1 </ sub > as the full subcategory of C consisting of those objects X of C for which ε < sub > X </ sub > is an isomorphism, and define D < sub > 1 </ sub > as the full subcategory of D consisting of those objects Y of D for which η < sub > Y </ sub > is an isomorphism.

C *- enveloping algebra as follows: Define a real valued function on A by

Let be the sheaf of holomorphic functions on C. Define the hyperfunctions on the real line by

Define ν < sub > p </ sub >( n ) as the exponent of the highest power of the prime p that divides n. I. e.

Define f ( a + bi ) = a < sup > 2 </ sup > + b < sup > 2 </ sup >, the squared norm of the Gaussian integer a + bi.

Define f ( a + bω ) = a < sup > 2 </ sup > − ab + b < sup > 2 </ sup >, the norm of the Eisenstein integer a + bω.

Define, where is the discrete valuation corresponding to the ideal P < sub > i </ sub >.

* Define a ≤ b as a < b or a =

* Define a b as " not b < a " ( i. e., take the inverse complement of the relation ), which corresponds to defining a ~ b as " neither a < b nor b < a "; these relations and ~ are in general not transitive ; however, if they are, ~ is an equivalence ; in that case "<" is a strict weak order.

Define f := f < sub > 1 </ sub > ∘ p < sub > 1 </ sub > + f < sub > 2 </ sub > ∘ p < sub > 2 </ sub >.

Define a data matrix, X < sup > T </ sup >, with zero empirical mean ( the empirical ( sample ) mean of the distribution has been subtracted from the data set ), where each of the n rows represents a different repetition of the experiment, and each of the m columns gives a particular kind of datum ( say, the results from a particular probe ).

Define f: R < sup > n </ sup > → R by f ( x ) = x < sup > T </ sup > M x.

Define a map from K < sup >×</ sup > to the set of all nonzero fractional ideals of R by sending every element to the principal ( fractional ) ideal it generates.

Define now a strictly increasing chain < math >( A_

Define f: l < sup >∞</ sup > → l < sup >∞</ sup > as the shift f ( x < sub > 1 </ sub >, x < sub > 2 </ sub >,...)

Define f ( n ) = | n |, the absolute value of n.

* Define to be the minimum number of moves required to transfer n disks using r pegs

:: Kakeya set conjecture: Define a Besicovitch set in R < sup > n </ sup > to be a set which contains a unit line segment in every direction.

Define to be the cylinder of length 1, radius, centered at the point a ∈ R < sup > n </ sup >, and whose long side is parallel to the direction of the unit vector e ∈ S < sup > n-1 </ sup >.

Define an ( n, k )-Besicovitch set K to be a compact set in R < sup > n </ sup > containing a translate of every k-dimensional unit disk which has Lebesgue measure zero.

Define f < sup > n </ sup > as the n-th iterate of f, where n is a non-negative integer, by:

( 2 ) Define for all n belonging to the reals.

Let be a basis for V. Define the n × n matrix A by.

Consider T to be a differentiable multilinear map of smooth sections α < sup > 1 </ sup >, α < sup > 2 </ sup >, ..., α < sup > q </ sup > of the cotangent bundle T * M and of sections X < sub > 1 </ sub >, X < sub > 2 </ sub >, ... X < sub > p </ sub > of the tangent bundle TM, written T ( α < sup > 1 </ sup >, α < sup > 2 </ sup >, ..., X < sub > 1 </ sub >, X < sub > 2 </ sub >, ...) into R. Define the Lie derivative of T along Y by the formula

Define a projection map π < sub > ρ </ sub >: E → X by π < sub > ρ </ sub >() = π ( p ).

Let X be a vector field on M. Choose any right-invariant lift to the tangent bundle of P. Define

* Define a distance function between any two non-empty sets X and Y of M by:

To see this, let X be an H-space with identity e and let f and g be loops at e. Define a map F: × → X by F ( a, b )

Define f ( x ) = 1 for all nonzero x.

* Name Forms — Define rules for the set of attributes that should be included in the RDN for an entry.

* Define truth just for the sentences in that subset.

Douglas claimed in his 1993 book Unfinished Business that speed was a key strategy for achieving radical economic change: " Define your objectives clearly, and move towards them in quantum leaps, otherwise the interest groups will have time to mobilise and drag you down ".

The essence of this pattern is to " Define an interface for creating an object, but let the classes that implement the interface decide which class to instantiate.

This permits an alternative definition for the ( general ) radical of an ideal I in R. Define Rad ( I ) as the preimage of N ( R / I ), the nilradical of R / I, under the projection map R → R / I.

* A Working Lexicon for the Tele-Intensive Care Unit: We Need to Define Tele-Intensive Care Unit to Grow and Understand It

# Define a long-running transaction model that is based on proven techniques like compensation actions and scoping to support failure recovery for parts of long-running business processes.

Define a relation R < sub > L </ sub > on strings by the rule that x R < sub > L </ sub > y if there is no distinguishing extension for x and y.

Define a vector v to have weight if for all λ in the weight lattice.

Define a subbase of open sets G < sub > x </ sub > for any integer x to be G < sub > x </ sub > = O < sub >

** Thomas Newman and Peter Gabriel for Define Dancing, from WALL-E performed by various artists.

*( j ) Define procedures for recognition of academic degrees awarded by other higher education institutions ;

Define if for all and let denote the probability of a jump from to.

Define as the generalized sum of the observable over the degrees of freedom of the single component ( sum for discrete variables, integrals for continuous ones ).

* Ainslie T. Embree, " The Function of the Rashtriya Swayamsevak Sangh: To Define the Hindu Nation ", in Accounting for Fundamentalisms, The Fundamentalism Project 4, ed.

* Define for every odd integer m.

Define, for all x in E,.

Define the rejection region of the null hypothesis for the NP test as

# Define the project scope-Evaluate mission and objectives for the project.